Skip to main content
Skip header

Special Topics in Mathematics

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code230-0403/01
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *Second Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites There are no prerequisites or co-requisites for this course unit
Name of Lecturer(s)Personal IDName
DLO44Mgr. Dagmar Dlouhá, Ph.D.
CER365doc. Ing. Martin Čermák, Ph.D.
DUB02RNDr. Viktor Dubovský, Ph.D.
Basics of vector calculus. Functions of several variables: partial differentiation, extremal values. Integral calculus of functions of two variables and its application. Line integral and its applications. Basics of vector fields.
Learning Outcomes of the Course Unit
Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to
analyze problems, distinguish between important and unimportant, suggest a
method of solution, verify each step of a method, generalize achieved results,
analyze correctness of achieved results with respect to given conditions, apply
these methods while solving technical problems, understand that mathematical
methods and theoretical advancements outreach the field mathematics.
Course Contents
1st Vector calculus, scalar, cross and triple product, vector functions.
2nd Differential calculus of functions of two or more real variables: domain, graph, limit and continuity.
3rd Partial derivatives, total differential, tangent plane and normal to a surface.
4th Implicit function and its derivatives.
5th Extremes of functions, calculation via derivatives.
6th Constrained extremes, Lagrange's method.
7th Global extremes. Taylor's theorem.
8th Two-dimensional integrals on a rectangle and on a general domain.
9th Calculations of two-dimensional integrals, applications in geometry and physics.
10th Three-dimensional integrals, calculation and application.
11th Line integral of the first and second kind, calculation methods.
12th Applications of curved integrals, Green's theorem, independence of the integration path.
13th Surface integrals and their calculation.
14th Introduction to the field theory: gradient, potential, divergence rotation, Gauss-Ostrogradsky's and Stoke's theorem.
Recommended or Required Reading
Required Reading:
KREML, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X.
KUČERA, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1.
HARSHBARGER, Ronald; REYNOLDS, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1.
BURDA, P., KREML, P.: Diferenciální počet funkcí jedné proměnné (Matematika
IIa). Učební texty VŠB – TU Ostrava, 2004, ISBN 80-248-0634-7.
KUČERA, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1.
Recommended Reading:
JAMES, G.: Modern Engineering Mathematics, Addison-Wesley, 1992, 0-201-1805456.
DOLEŽALOVÁ, Jarmila: Mathematics I, VŠB - TUO, Ostrava 2005, 80-248-0796-3.
MOORE,C: Math quations and inequalities, Science & Nature, 2014.
JAMES, G.: Modern Engineering Mathematics. Addison – Wesley Publishing
Company, Wokingham, 1994, ISBN 0-201-18504-5.
ŠKRÁŠEK, J. - TICHÝ, Z.: Základy aplikované matematiky I, II, III, SNTL, Praha 1990.
BURDA, P., DOLEŽALOVÁ, J.: Cvičení z matematiky IV. Skriptum VŠB-TUO, Ostrava 2002,ISBN 80-248-0028-4.
JAMES, G.: Modern Engineering Mathematics, Addison-Wesley, 1992, 0-201-1805456.
DOBROVSKÁ, V., VRBICKÝ, J.: Diferenciální počet funkcí více proměnných,
Matematika IIb. Učební texty VŠB – TUO, Ostrava, 2004, ISBN 80-248-0656-8.
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit20 5
        ExaminationExamination80 (80)30
                Písemná zkouškaWritten examination60 25
                Ústní zkouškaOral examination20 5